Load libraries

library(tidyverse) # data manipulation
library(ggpubr) # producing data exploratory plots
library(modelsummary) # descriptive data 
library(glmmTMB) # running generalised mixed models 
library(DHARMa) # model diagnostics 
library(performance) # model diagnostics  
library(ggeffects) # partial effect plots 
library(car) # running Anova on model 
library(emmeans) # post-hoc analysis

Import data

df_adults <- read_csv("resp_results_adults.csv")
df_jresp <- read_csv("resp_results_juveniles.csv")

Data manipulation

Adults

df_adults_cleaned <- df_adults |> 
  mutate(FISH_ID = factor(FISH_ID), 
         Sex = factor(Sex), 
         Population = factor(Population), 
         Tank = factor(Tank), 
         Chamber = factor(Chamber), 
         System =factor(System), 
         Temperature =factor(Temperature), 
         True_resting=factor(True_resting)) 

df_males <- df_adults_cleaned |> 
  filter(Sex == "M")
df_females <- df_adults_cleaned |> 
  filter(Sex == "F")

df_adults_cleaned2 <- df_males |> 
  full_join(select(df_females, c("Tank","Temperature","Mass","Resting","Max","AAS","FISH_ID","Sex")), by="Tank") |> 
  mutate(Temperature.x = coalesce(Temperature.x, Temperature.y), 
         FISH_ID.x = coalesce(FISH_ID.x, FISH_ID.y),
         Sex.x = coalesce(Sex.x, Sex.y),
         Resting.midpoint = (Resting.x+Resting.y)/2, 
         Max.midpoint = (Max.x+Max.y)/2, 
         AAS.midpoint = (AAS.x+AAS.y)/2)

Juveniles

df_jresp$Population <-  fct_collapse(df_jresp$Population, 
                                      `Vlassof cay`= c("Vlassof reef", "Vlassof", "Vlassof Cay", "Vlassof cay"), 
                                      `Arlington reef` = c("Arlington reef","Arlginton reef")) 

#df_jresp$Female <-  fct_collapse(df_jresp$Female, 
                                  #`CARL359`= c("CARL359", "CARL59")) 


df_jresp2 <-  df_jresp |> 
  unite("F0", c("Male","Female"), sep="_", remove=FALSE) |>
  mutate(across(1:7, factor), 
         Temperature = factor(Temperature), 
         True_resting = factor(True_resting)) 

#df_jresp2_rest <- df_jresp2 |> 
  #filter(True_resting == "Y")

Merging dataframes

temp1a <- df_jresp2 |> 
  mutate(FISH_ID.x = Male)
temp1b <- df_jresp2 |> 
  mutate(FISH_ID.y = Female)
temp2a <- temp1a |> 
  left_join(select(df_adults_cleaned2, c("FISH_ID.x",
                                          "Sex.x",
                                          "Resting.x", 
                                          "Max.x", 
                                          "AAS.x", 
                                          "Mass.x")), 
                    by="FISH_ID.x")
temp2b <- temp1b |> 
  left_join(select(df_adults_cleaned2, c("FISH_ID.y",
                            "Sex.y",
                            "Resting.y", 
                            "Max.y", 
                            "AAS.y", 
                            "Mass.y")), 
                   by="FISH_ID.y") 
df_merged <- temp2a |> 
  left_join(select(temp2b, c("Clutch","Replicate", 
                             "FISH_ID.y",
                             "Resting.y", 
                             "Max.y", 
                             "AAS.y", 
                             "Mass.y")), 
            by=c("Clutch","Replicate"))
df <- df_merged |> 
  mutate(Resting_MALE =Resting.x, 
         Max_MALE =Max.x, 
         AAS_MALE =AAS.x, 
         Mass_MALE =Mass.x, 
         FISH_ID.y =FISH_ID.x,#makes more sense for males to be .y instead of .x
         FISH_ID.x =FISH_ID.x, 
         Resting_FEMALE =Resting.y, 
         Max_FEMALE =Max.y, 
         AAS_FEMALE =AAS.y, 
         Mass_FEMALE =Mass.y) |> 
  mutate(Resting_MID =(Resting_MALE+Resting_FEMALE)/2, 
         Max_MID =(Max_MALE+Max_FEMALE)/2, 
         AAS_MID =(AAS_MALE+AAS_FEMALE)/2) # easier to do it again

Exploratory analysis

Offspring-Male

plot1 <- ggplot(df, aes(x=Resting_MALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") + 
  xlab("") + 
  ylab("Resting (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot2 <- ggplot(df, aes(x=Max_MALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("") + 
  ylab("Max (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot3 <- ggplot(df, aes(x=AAS_MALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("") + 
  ylab("AAS (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot4 <- ggplot(df, aes(x=Resting_MALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") + 
  xlab("Resting (offspring)") + 
  ylab("Resting (parental-male)") +
  theme_classic() + 
  theme(legend.position = "bottom")

plot5 <- ggplot(df, aes(x=Max_MALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("Max (offspring)") + 
  ylab("Max (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot6 <- ggplot(df, aes(x=AAS_MALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("AAS (offspring)") + 
  ylab("AAS (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none') 

ggarrange(plot1, plot2, plot3, 
          plot4, plot5, plot6,
          ncol = 3, 
          nrow = 3)

Offspring-Female

plot1 <- ggplot(df, aes(x=Resting_FEMALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") + 
  xlab("") + 
  ylab("Resting (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot2 <- ggplot(df, aes(x=Max_FEMALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("") + 
  ylab("Max (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot3 <- ggplot(df, aes(x=AAS_FEMALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("") + 
  ylab("AAS (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot4 <- ggplot(df, aes(x=Resting_FEMALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") + 
  xlab("Resting (offspring)") + 
  ylab("Resting (parental-female)") +
  theme_classic() + 
  theme(legend.position = "bottom")

plot5 <- ggplot(df, aes(x=Max_FEMALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("Max (offspring)") + 
  ylab("Max (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot6 <- ggplot(df, aes(x=AAS_FEMALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("AAS (offspring)") + 
  ylab("AAS (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none') 

ggarrange(plot1, plot2, plot3, 
          plot4, plot5, plot6,
          ncol = 3, 
          nrow = 3)

Offspring-Midpoint

plot1 <- ggplot(df, aes(x=Resting_MID, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") + 
  xlab("") + 
  ylab("Resting (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot2 <- ggplot(df, aes(x=Max_MID, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("") + 
  ylab("Max (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot3 <- ggplot(df, aes(x=AAS_MID, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("") + 
  ylab("AAS (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot4 <- ggplot(df, aes(x=Resting_MID, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") + 
  xlab("Resting (offspring)") + ylab("Resting (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot5 <- ggplot(df, aes(x=Max_MID, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("Max (offspring)") + ylab("Max (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot6 <- ggplot(df, aes(x=AAS_MID, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("AAS (offspring)") + ylab("AAS (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none') 

ggarrange(plot1, plot2, plot3, 
          plot4, plot5, plot6,
          ncol = 3, 
          nrow = 3, 
          common.legend = TRUE)

Descriptive statistics

Juveniles - overview

Overview

tinytable_z0vf386bmm8l4rwdpbra
Population 27 28.5 30
Arlington reef 60 43 53
Pretty patches 26 21 34
Sudbury reef 27 15 16
Vlassof cay 26 10 28 
datasummary(Factor(F0) ~ Factor(Temperature), 
            data = df, 
            fmt = "%.0f")
tinytable_irrf0e8sbj2w05k5o7cv
F0 27 28.5 30
CARL217_CARL226 0 8 0
CARL218_CARL222 0 0 13
CARL230_CARL235 14 0 0
CARL233_CARL215 0 0 8
CARL237_CARL219 10 0 0
CARL241_CARL239 15 0 0
CARL249_CARL360 0 0 8
CARL335_CARL359 0 14 0
CARL338_CARL345 0 8 0
CARL344_CARL370 0 0 16
CARL354_CARL355 21 0 0
CARL360_CARL249 0 0 8
CARL367_CARL363 0 7 0
CARL369_CARL349 0 6 0
CPRE189_CPRE202 0 0 15
CPRE372_CPRE209 6 0 0
CPRE372_CPRE370 8 0 0
CPRE375_CPRE377 12 0 0
CPRE391_CPRE390 0 0 6
CPRE447_CPRE452 0 0 13
CPRE453_CPRE459 0 7 0
CPRE521_CPRE524 0 7 0
CPRE550_CPRE533 0 7 0
CSUD002_CSUD213 0 8 0
CSUD009_CSUD212 14 0 0
CSUD013_CSUD017 13 0 0
CSUD016_CSUD078 0 7 0
CSUD312_CSUD304 0 0 16
CVLA049_CVLA098 0 10 0
CVLA089_CVLA059 0 0 7
CVLA102_CVLA466 6 0 0
CVLA106_CVLA091 0 0 15
CVLA468_CVLA477 13 0 0
CVLA486_CVLA463 7 0 0
CVLA498_CVLA493 0 0 6

Juveniles

Resting oxygen uptake

tinytable_j89pji6zxznf9wbkqly3
Temperature NUnique mean median min max sd Histogram
27 135 0.21 0.21 0.08 0.64 0.07 ▃▆▇▅▁▁
28.5 89 0.23 0.23 0.09 0.47 0.08 ▂▄▆▆▇▄▁▁ ▁
30 131 0.23 0.23 0.06 0.40 0.07 ▁▂▃▆▇▅▆▄▁▁

Maximum oxygen uptake

tinytable_xw84het460w5x5kvmzb6
Temperature NUnique mean median min max sd Histogram
27 132 0.58 0.55 0.27 1.66 0.19 ▄▇▆▃▁
28.5 85 0.65 0.64 0.24 1.08 0.18 ▂▄▇▇▇▃▃▂▂
30 130 0.65 0.64 0.16 1.29 0.19 ▂▃▇▅▆▃▁

Absolute aerobic scope

tinytable_v4lwwa0r8y7k4tj07sl5
Temperature NUnique mean median min max sd Histogram
27 128 0.37 0.34 0.14 1.02 0.14 ▃▇▇▄▃▂
28.5 85 0.42 0.39 0.10 0.79 0.15 ▁▃▅▇▄▃▅▃▁▁
30 130 0.42 0.41 0.09 0.99 0.15 ▁▄▆▅▇▃▁

Adults - overview

Overview

datasummary(Factor(Population) ~ Factor(Temperature), 
            data = df_adults_cleaned, 
            fmt = "%.0f")
tinytable_qd42z7g0wgeqqzsx1xi5
Population 27 28.5 30
Arlington reef 8 7 4
Pretty patches 4 6 4
Sudbury reef 4 3 2
Vlassof cay 6 2 5 
datasummary(Factor(Population) ~ Factor(Temperature)*Factor(Sex), 
            data = df_adults_cleaned, 
            fmt = "%.0f")
tinytable_s5u613sbtxfxxdwntwhe
27 28.5 30
Population F M F M F M
Arlington reef 4 4 2 5 2 2
Pretty patches 2 2 3 3 3 1
Sudbury reef 2 2 1 2 1 1
Vlassof cay 3 3 1 1 3 2

Pairs

datasummary(Factor(Population)*Factor(Temperature.x) ~ AAS.midpoint*(NUnique), 
            data = df_adults_cleaned2, 
            fmt = "%.0f")
tinytable_49xketrpf8luvaxf29fx
Population Temperature.x NUnique
Arlington reef 27 3
28.5 2
30 2
Pretty patches 27 2
28.5 3
30 1
Sudbury reef 27 2
28.5 2
30 1
Vlassof cay 27 3
28.5 1
30 2

Adults

Resting oxygen uptake

tinytable_igkga8kavi5g3n5kx64a
Temperature NUnique mean median min max sd Histogram
27 22 6.29 6.06 3.82 10.09 1.56 ▂▂▃▇▂▂▁▁▁▁
28.5 18 6.49 6.96 4.35 8.49 1.45 ▇▂▅▂▃▃▅▃
30 15 7.29 7.20 5.14 9.15 1.46 ▅▂▇▂▂▂▇▇

Maximum oxygen uptake

tinytable_ttwnruq3kruj2cq3keew
Temperature NUnique mean median min max sd Histogram
27 22 16.58 16.91 9.70 22.06 3.36 ▃▃▅▅▃▃▅▇▂
28.5 18 17.09 17.23 11.04 28.39 3.94 ▅▂▅▇▇▃▂
30 15 16.48 16.83 11.78 21.24 2.82 ▂▃▂▃▇▂▂▃▂

Absolute aerobic scope

tinytable_d6ax65pxap5ulbr9srwm
Temperature NUnique mean median min max sd Histogram
27 22 10.29 10.26 3.85 16.28 3.14 ▃▁▄▇▃▆▃▃▁
28.5 18 10.59 9.66 6.11 20.44 3.66 ▅▅▇▇▃▂▂
30 15 9.19 9.16 4.36 12.77 2.91 ▃▂▅▂▂▂▃▇

Fit Models [random factors]

model1 <- glmmTMB(Max ~ (1|Clutch), 
                  family="gaussian",
                  data = df) 

model2 <- glmmTMB(Max ~ (1|Clutch) + (1|Population), 
                  family="gaussian",
                  data = df) 

model3 <- glmmTMB(Max ~ (1|Clutch) + (1|Chamber), 
                  family="gaussian",
                  data = df) 

model4 <- glmmTMB(Max ~ (1|Clutch) + (1|Population) + (1|Chamber), 
                  family="gaussian",
                  data = df)
Model selection
AIC(model1, model2, model3, model4, k=2)
BIC(model1, model2, model3, model4)

Model1 performs the best therefore only Clutch will be used as a random factor in future models

Relationships

Offspring-Male

Fit model [fixed factors]

After figuring out which random factors will be incorporated into the model we will start to examine out fixed factors. Some fixed factors such as Max_(FE)MALE and TEMPERATURE will be essential to answering questions we have around heritability. Another factor that will be included is Dry_mass - which it should be pointed out in this experiment refers to the mass of fish after they were blotted dry with paper towel rather than completely dried out. Larger fish consume more oxygen, therefore, we need to account for this known relationship within our model. Out model will look something like this:

Max ~ Max_MALE*Temprature + scale(Dry_mass)

If we had alternative hypotheses to test would would do so at this stage. But in this instance the experiment was designed to answer a specific question via limiting potential covariates.

model1.1 <- glmmTMB(Max ~ Max_MALE*Temperature+scale(Dry_mass) + (1|Clutch), 
                    family="gaussian", 
                    data=df)

Great now lets check how out model performed via model validation techniques

Model validation

To check out model performance we will be using two different packages that perform model diagnositics. The packages used here are just examples, there are other packages out there that can provide the same function.

DHARMa

model1.1 |> 
  simulateResiduals(plot=TRUE) 
## qu = 0.75, log(sigma) = -2.159312 : outer Newton did not converge fully.

## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help. 
##  
## Scaled residual values: 0.408 0.264 0.104 0.096 0.064 0.936 0.036 0.22 0.156 0.816 0.616 0.38 0.264 0.368 0.456 0.132 0.412 0.112 0.324 0.764 ...
model1.1 |> 
  testResiduals(plot=TRUE)

## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.078982, p-value = 0.06156
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0009, p-value = 0.96
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 2, observations = 279, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.0008693156 0.0256536077
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                            0.007168459
## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.078982, p-value = 0.06156
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0009, p-value = 0.96
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 2, observations = 279, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.0008693156 0.0256536077
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                            0.007168459

performance

model1.1 |> check_model(detrend=FALSE)
## `check_outliers()` does not yet support models of class `glmmTMB`.

Partial effect plots

model1.1 |> ggemmeans(~Max_MALE|Temperature) |> 
  plot(add.data =FALSE)

Model investigations

summary

model1.1 |> summary()
##  Family: gaussian  ( identity )
## Formula:          Max ~ Max_MALE * Temperature + scale(Dry_mass) + (1 | Clutch)
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   -332.3   -299.6    175.2   -350.3      270 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance  Std.Dev.
##  Clutch   (Intercept) 0.0005792 0.02407 
##  Residual             0.0161543 0.12710 
## Number of obs: 279, groups:  Clutch, 42
## 
## Dispersion estimate for gaussian family (sigma^2): 0.0162 
## 
## Conditional model:
##                           Estimate Std. Error z value Pr(>|z|)    
## (Intercept)               0.539070   0.059170   9.110   <2e-16 ***
## Max_MALE                  0.001857   0.003592   0.517    0.605    
## Temperature28.5           0.092178   0.103146   0.894    0.372    
## Temperature30             0.296710   0.134168   2.211    0.027 *  
## scale(Dry_mass)           0.128647   0.008058  15.966   <2e-16 ***
## Max_MALE:Temperature28.5 -0.001864   0.006388  -0.292    0.770    
## Max_MALE:Temperature30   -0.010474   0.008375  -1.251    0.211    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA

model1.1 |> Anova()

confint

model1.1 |> confint()
##                                   2.5 %      97.5 %     Estimate
## (Intercept)                 0.423098516 0.655041731  0.539070124
## Max_MALE                   -0.005182572 0.008897225  0.001857327
## Temperature28.5            -0.109985074 0.294341715  0.092178320
## Temperature30               0.033745657 0.559674722  0.296710190
## scale(Dry_mass)             0.112854304 0.144439320  0.128646812
## Max_MALE:Temperature28.5   -0.014384423 0.010656794 -0.001863815
## Max_MALE:Temperature30     -0.026889718 0.005941254 -0.010474232
## Std.Dev.(Intercept)|Clutch  0.007632105 0.075892214  0.024066934

r-squared

model1.1 |> r2_nakagawa()
## # R2 for Mixed Models
## 
##   Conditional R2: 0.538
##      Marginal R2: 0.522

Pairwise comparisons

emmeans [Temperature]

model1.1 |> emmeans(pairwise ~ Temperature, type="response") |> 
  summary(by=NULL, adjust="sidak", infer=TRUE)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
##  Temperature emmean     SE  df lower.CL upper.CL t.ratio p.value
##  27           0.575 0.0123 270    0.546    0.605  46.671  <.0001
##  28.5         0.638 0.0164 270    0.599    0.677  38.906  <.0001
##  30           0.705 0.0173 270    0.664    0.747  40.735  <.0001
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 3 estimates 
## P value adjustment: sidak method for 3 tests 
## 
## $contrasts
##  contrast                        estimate     SE  df lower.CL upper.CL t.ratio
##  Temperature27 - Temperature28.5  -0.0625 0.0205 270   -0.112 -0.01333  -3.054
##  Temperature27 - Temperature30    -0.1301 0.0213 270   -0.181 -0.07893  -6.108
##  Temperature28.5 - Temperature30  -0.0676 0.0241 270   -0.126 -0.00965  -2.803
##  p.value
##   0.0074
##   <.0001
##   0.0162
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 3 estimates 
## P value adjustment: sidak method for 3 tests

Summary figure

om.max <- emmeans(model1.1, ~Max_MALE*Temperature, 
                   at =list(Max_MALE =seq(from=9, to =21, by=.2)))

om.max.df <- as.data.frame(om.max)

om.max.obs <- drop_na(df, Max_MALE, Max) |> 
  mutate(Pred =predict(model1.1, re.form =NA, type='response'), 
         Resid =residuals(model1.1, type ="response"), 
         Fit =Pred + Resid) 

om.max.obs.summarize <- om.max.obs |> 
  group_by(Clutch, Temperature) |> 
  summarise(mean.max =mean(Max, na.rm=TRUE),
            mean.max_male =mean(Max_MALE, na.rm=TRUE),
            sd.max =sd(Max, na.rm =TRUE), 
            n.max = n()) |> 
  mutate(se.max = sd.max / sqrt(n.max), 
         lower.ci.max =mean.max - qt(1 - (0.05/2), n.max -1) * se.max, 
         upper.ci.max =mean.max + qt(1 - (0.05/2), n.max - 1) * se.max)|>
  ungroup()
## `summarise()` has grouped output by 'Clutch'. You can override using the
## `.groups` argument.
ggplot(data =om.max.df, aes(y=emmean, x=Max_MALE)) + 
  stat_smooth(aes(color=Temperature), 
              method = "lm") + 
  geom_pointrange(data = om.max.obs.summarize, aes(y =mean.max, x=mean.max_male, 
                                                    ymin =lower.ci.max, 
                                                    ymax =upper.ci.max, color = Temperature), 
                  alpha =0.2) + 
  facet_wrap(~Temperature) +
  theme_classic() + 
  theme(legend.position ="bottom")
## `geom_smooth()` using formula = 'y ~ x'

Offspring-female

Fit model [fixed factors]

fmodel1.1 <- glmmTMB(Max ~ Max_FEMALE*Temperature+scale(Dry_mass) + (1|Clutch), 
                    family="gaussian", 
                    data=df)

Great now lets check how out model performed via model validation techniques

Model validation

To check out model performance we will be using two different packages that perform model diagnositics. The packages used here are just examples, there are other packages out there that can provide the same function.

DHARMa

fmodel1.1 |> 
  simulateResiduals(plot=TRUE) 

## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help. 
##  
## Scaled residual values: 0.204 0.844 0.612 0.436 0.336 0.356 0.44 0.136 0.388 0.152 0.324 0.808 0.696 0.188 0.136 0.2 0.456 0.376 0.108 0.288 ...
fmodel1.1 |> 
  testResiduals(plot=TRUE)

## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.088444, p-value = 0.02928
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.001, p-value = 0.968
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 3, observations = 270, p-value = 0.4797
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.002297266 0.032126194
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.01111111
## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.088444, p-value = 0.02928
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.001, p-value = 0.968
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 3, observations = 270, p-value = 0.4797
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.002297266 0.032126194
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.01111111

performance

fmodel1.1 |> check_model(detrend=FALSE)
## `check_outliers()` does not yet support models of class `glmmTMB`.

Partial effect plots

fmodel1.1 |> ggemmeans(~Max_FEMALE|Temperature) |> 
  plot(add.data =FALSE)

Model investigations

summary

fmodel1.1 |> summary()
##  Family: gaussian  ( identity )
## Formula:          
## Max ~ Max_FEMALE * Temperature + scale(Dry_mass) + (1 | Clutch)
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   -303.0   -270.6    160.5   -321.0      261 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Clutch   (Intercept) 0.000714 0.02672 
##  Residual             0.017190 0.13111 
## Number of obs: 270, groups:  Clutch, 41
## 
## Dispersion estimate for gaussian family (sigma^2): 0.0172 
## 
## Conditional model:
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 0.534019   0.066284   8.057 7.85e-16 ***
## Max_FEMALE                  0.002473   0.003991   0.620   0.5355    
## Temperature28.5             0.073664   0.125334   0.588   0.5567    
## Temperature30               0.232860   0.130817   1.780   0.0751 .  
## scale(Dry_mass)             0.134599   0.008626  15.604  < 2e-16 ***
## Max_FEMALE:Temperature28.5 -0.001683   0.006721  -0.250   0.8023    
## Max_FEMALE:Temperature30   -0.006893   0.007548  -0.913   0.3611    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA

fmodel1.1 |> Anova()

confint

fmodel1.1 |> confint()
##                                   2.5 %      97.5 %     Estimate
## (Intercept)                 0.404104070 0.663933330  0.534018700
## Max_FEMALE                 -0.005349958 0.010295710  0.002472876
## Temperature28.5            -0.171987009 0.319315162  0.073664076
## Temperature30              -0.023536245 0.489256419  0.232860087
## scale(Dry_mass)             0.117693449 0.151505533  0.134599491
## Max_FEMALE:Temperature28.5 -0.014856436 0.011490229 -0.001683103
## Max_FEMALE:Temperature30   -0.021686920 0.007900064 -0.006893428
## Std.Dev.(Intercept)|Clutch  0.009334660 0.076489988  0.026720928

r-squared

fmodel1.1 |> r2_nakagawa()
## # R2 for Mixed Models
## 
##   Conditional R2: 0.540
##      Marginal R2: 0.521

Summary figure

om.max <- emmeans(fmodel1.1, ~Max_FEMALE*Temperature, 
                   at =list(Max_FEMALE =seq(from=10, to =30, by=.2)))

om.max.df <- as.data.frame(om.max)

om.max.obs <- drop_na(df, Max_FEMALE, Max) |> 
  mutate(Pred =predict(fmodel1.1, re.form =NA, type='response'), 
         Resid =residuals(fmodel1.1, type ="response"), 
         Fit =Pred + Resid) 

om.max.obs.summarize <- om.max.obs |> 
  group_by(Clutch, Temperature) |> 
  summarise(mean.max =mean(Max, na.rm=TRUE),
            mean.max_female =mean(Max_FEMALE, na.rm=TRUE),
            sd.max =sd(Max, na.rm =TRUE), 
            n.max = n()) |> 
  mutate(se.max = sd.max / sqrt(n.max), 
         lower.ci.max =mean.max - qt(1 - (0.05/2), n.max -1) * se.max, 
         upper.ci.max =mean.max + qt(1 - (0.05/2), n.max - 1) * se.max)|>
  ungroup()
## `summarise()` has grouped output by 'Clutch'. You can override using the
## `.groups` argument.
ggplot(data =om.max.df, aes(y=emmean, x=Max_FEMALE)) + 
  stat_smooth(aes(color=Temperature), 
              method = "lm") + 
  geom_pointrange(data = om.max.obs.summarize, aes(y =mean.max, x=mean.max_female, 
                                                    ymin =lower.ci.max, 
                                                    ymax =upper.ci.max, color = Temperature), 
                  alpha =0.2) + 
  facet_wrap(~Temperature) +
  theme_classic() + 
  theme(legend.position ="bottom")
## `geom_smooth()` using formula = 'y ~ x'

Offspring-midpoint

Fit model [fixed factors]

mid_model1.1 <- glmmTMB(Max ~ Max_MID*Temperature+scale(Dry_mass) + (1|Clutch), 
                    family="gaussian", 
                    data=df)

Great now lets check how out model performed via model validation techniques

Model validation

To check out model performance we will be using two different packages that perform model diagnositics. The packages used here are just examples, there are other packages out there that can provide the same function.

DHARMa

mid_model1.1 |> 
  simulateResiduals(plot=TRUE) 

## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help. 
##  
## Scaled residual values: 0.16 0.824 0.68 0.408 0.28 0.324 0.48 0.112 0.448 0.104 0.308 0.74 0.7 0.168 0.156 0.188 0.384 0.284 0.128 0.244 ...
mid_model1.1 |> 
  testResiduals(plot=TRUE)

## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.083174, p-value = 0.07029
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0021, p-value = 0.928
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 1, observations = 242, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.0001046136 0.0228070249
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                            0.004132231
## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.083174, p-value = 0.07029
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0021, p-value = 0.928
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 1, observations = 242, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.0001046136 0.0228070249
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                            0.004132231

performance

mid_model1.1 |> check_model(detrend=FALSE)
## `check_outliers()` does not yet support models of class `glmmTMB`.

Partial effect plots

mid_model1.1 |> ggemmeans(~Max_MID|Temperature) |> 
  plot(add.data =FALSE)

Model investigations

summary

mid_model1.1 |> summary()
##  Family: gaussian  ( identity )
## Formula:          Max ~ Max_MID * Temperature + scale(Dry_mass) + (1 | Clutch)
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   -287.9   -256.5    153.0   -305.9      233 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance  Std.Dev.
##  Clutch   (Intercept) 0.0003232 0.01798 
##  Residual             0.0162346 0.12741 
## Number of obs: 242, groups:  Clutch, 37
## 
## Dispersion estimate for gaussian family (sigma^2): 0.0162 
## 
## Conditional model:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept)              0.519208   0.063814   8.136 4.08e-16 ***
## Max_MID                  0.003426   0.003892   0.880    0.379    
## Temperature28.5          0.120848   0.137866   0.877    0.381    
## Temperature30            0.289517   0.182631   1.585    0.113    
## scale(Dry_mass)          0.131236   0.008721  15.048  < 2e-16 ***
## Max_MID:Temperature28.5 -0.004280   0.007688  -0.557    0.578    
## Max_MID:Temperature30   -0.010014   0.011090  -0.903    0.367    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA

mid_model1.1 |> Anova()

confint

mid_model1.1 |> confint()
##                                   2.5 %     97.5 %     Estimate
## (Intercept)                 0.394134940 0.64428094  0.519207942
## Max_MID                    -0.004201702 0.01105304  0.003425667
## Temperature28.5            -0.149363524 0.39105951  0.120847993
## Temperature30              -0.068432670 0.64746601  0.289516669
## scale(Dry_mass)             0.114142718 0.14832912  0.131235921
## Max_MID:Temperature28.5    -0.019348111 0.01078842 -0.004279846
## Max_MID:Temperature30      -0.031750376 0.01172141 -0.010014483
## Std.Dev.(Intercept)|Clutch  0.002229782 0.14494421  0.017977596

r-squared

mid_model1.1 |> r2_nakagawa()
## # R2 for Mixed Models
## 
##   Conditional R2: 0.545
##      Marginal R2: 0.536

Summary figure

om.max <- emmeans(mid_model1.1, ~Max_MID*Temperature, 
                   at =list(Max_MID =seq(from=8, to =26, by=.2)))

om.max.df <- as.data.frame(om.max)

om.max.obs <- drop_na(df, Max_MID, Max) |> 
  mutate(Pred =predict(mid_model1.1, re.form =NA, type='response'), 
         Resid =residuals(mid_model1.1, type ="response"), 
         Fit =Pred + Resid) 

om.max.obs.summarize <- om.max.obs |> 
  group_by(Clutch, Temperature) |> 
  summarise(mean.max =mean(Max, na.rm=TRUE),
            mean.max_female =mean(Max_MID, na.rm=TRUE),
            sd.max =sd(Max, na.rm =TRUE), 
            n.max = n()) |> 
  mutate(se.max = sd.max / sqrt(n.max), 
         lower.ci.max =mean.max - qt(1 - (0.05/2), n.max -1) * se.max, 
         upper.ci.max =mean.max + qt(1 - (0.05/2), n.max - 1) * se.max)|>
  ungroup()
## `summarise()` has grouped output by 'Clutch'. You can override using the
## `.groups` argument.
ggplot(data =om.max.df, aes(y=emmean, x=Max_MID)) + 
  stat_smooth(aes(color=Temperature), 
              method = "lm") + 
  geom_pointrange(data = om.max.obs.summarize, aes(y =mean.max, x=mean.max_female, 
                                                    ymin =lower.ci.max, 
                                                    ymax =upper.ci.max, color = Temperature), 
                  alpha =0.2) + 
  facet_wrap(~Temperature) +
  theme_classic() + 
  theme(legend.position ="bottom")
## `geom_smooth()` using formula = 'y ~ x'